Roulette Probability Made Easier

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



13. MIXED CHAINS

Now, with a little bit of logic thinking and a calculator, you can use what you have learned above to make all those calculations for all the roulette-bets there are.
Instead of using the 18/37 fraction, you change the "18" to the "number of covered single numbers" in your bet.

Each trial can have their own bets:
Trial 1: Bet a Dozen (12/37)
Trial 2: Bet a 6-Street (6/37)
Trial 3: Bet Low (18/37)
Trial 4: Bet a Split (2/37)

What's the probability to hit ALL four?
Solution: (12/37) x (6/37) x (18/37) x (2/37) = 2,592 / 1,874,161 (Some 0.14%)

What's the probability to hit AT LEAST once?
First trial: 12/37 +
Second trial: (25/37) x (6/37) +
Third trial: (25/37) x (31/37) x (18/37) +
Fourth trial: (25/37) x (31/37) x (19/37) x (2/37) =

That is: (12/37) + ((25x6) / 37x37)) + ((25x31x18) / (37x37x37)) + ((25x31x19x2) / (37x37x37x37))
= 1,358,786 / 1,874,161 to be exact.



Or 72.5% rounded.


- Can you PLEASE explain?

Of course...

The first trial: The bet is a Dozen so you have a probability of 12/37 to hit. And a 25/37 probability to miss. Nothing special.

The second trial: First of all you lost the first trial; that's a 25/37 probability (see above). Then you have a 6/37 to hit the second trial.

*** The probability to hit at this trial is: The probability to MISS the previous trial times the probability to HIT this trial.
So the probability to hit at this trial is (25/37) x (6/37) = 150 / 1369.

*** The probability to miss at this trial is: The probability to MISS the previous trial times the probability to MISS this trial.
So the probability to miss at this trial is (25/37) x (31/37)

Do you understand the "25 / 37" - why is it there?
It's because you had lo lose the first trial to come to this, the second, trial. That was a 25/37 probability and therefore it has to be included.
It's the 25/37 results in the first trial that didn't hit.

A loss here therefore happens in (25/37) x (31/37) as that many results didn't hit here.
The 25/37 left from the first trial and now 31/37 left from here.
As they are combined, you have to multiply them.

REMEMBER:
The probability to hit at this trial is: The probability to MISS the previous trial times the probability to HIT this trial.
The probability to miss at this trial is: The probability to MISS the previous trial times the probability to MISS this trial.


The third trial: First of all you lost the second trial and the probability to do that was (25/37) x (31/37). See above.
Now you bet Low, that has a 18/37 probability to hit and therefore the calculation is:
To hit:  (25/37) x (31/37) x (18/37)
To miss: (25/37) x (31/37) x (19/37)


The fourth trial: Now you missed at the third trial as well and that was, as we saw above, a probability of (25/37) x (31/37) x (19/37).
And now you bet a 2-numbers split that has a 2/37 chance to hit. Calculations:
To hit: (25/37) x (31/37) x (19/37) x (2/37)

That is how the probability of 1,358,786 / 1,874,161 was calculated.
And if we have 1,358,786 chances to hit, there has to be 515,375 chances to miss (as 1,874,161 - 1,358,786 = 515,375)


The quicker (logic) way:
If you quit at any time you hit, you only have to calculate by the probability of a miss on ALL the four trials - if you don't miss all four, you obviously must have hit... right? So, for this four-misses event the calculation is:

(25/37) x (31/37) x (19/37) x (35/37) = 515,375 / 1,874,161.

And therefore the chance to hit is (1,874,161 - 515,375 =) 1,358,786 / 1,874,161

The same exactly.

Probably correct...

----------------------------------

As a complement to this document I have written a small probability calculator in JavaScript.
It is a HTML-page so it is easy to open it in your web-browser.

Download it from the members download area here:
nolinks://vlsroulette.com/downloads/?sa=view;id=167

You can calculate the probabilities to...

* Hit "this" trial
* Miss "this" trial
* Hit at least one trial
* Miss all trials


in as long a chain of trials you like with different bets for each.
Bet from one number to all - both 0- and 00-wheel.

Save the output by a simple copy-and-paste.

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



14. DEVIATION FROM THE AVERAGE

- YEAH YEAH YEAH! 18/37 is a theoretical thing! If I bet Red 37 times, will I hit 18 times? No! So what's good with all this???

The BAD thing is, what you correctly point out, that it's pure theoretical. It's the MATHEMATICAL AVERAGE for a large sample of results.

The GOOD with all the above is that you've learn the basics of how to calculate your true odds for every single bet in every possible situation.
And from here, we can dig a bit deeper into probability theory; you NEED to know that basic stuff before we can go on.


And yes; you suppose a sample of 37 results and you don't think there is exactly 18 Reds, 18 Blacks and one Zero there, like math says it should be.
And of course there aren't (probably). One or the other will probably be dominant. And if you check a lot of 37-spins samples you will find that sometimes Red is dominant and sometimes Black (probably not the Zero, though).

18 / 37 is just a mathematical average. It's the kind of figure you will have from examining a lot of 37-results samples.
But it's an average and can as such be used to measure the deviation from it.

The DEVIATION from the average.

If there are 22 Reds in that sample, the deviation for Red is +4 hits.
If there are only 12 Blacks the deviation for Black is -6 hits.
(And if both are true, the deviation for the Zero is +2 hits).

Red has +4 because 18 was expected but there were 22 hits.
Black has -6 because 18 was expected but there were only 12 hits.
Zero has +2 because only one was expected but there were 3 hits.

Now, mathematicians have invented something they call STANDARD DEVIATION (SD for short) that can be used for measuring the deviation in order to see if it is RANDOM or not.
Through count-less (literally) empirical studies and other means they have found it to be reliable and it is in fact the norm.
(Maybe a subjective one...)


One SD is a certain part of the whole. To show what I mean as an ILLUSTRATION (not a true example):
Suppose coin-tossing 100 times while recording the results. Now suppose doing that 1000 times. You have a sample of 1000 100-trials events.
Now, when you check those results (that all should be 50 heads and 50 tails according to math) you find that the vast majority has 47 to 53 heads. The deviation is +-3 hits for the majority.
You could very well call this "My Deviation" (MD for short) and now you can categorize all 1000 samples by their MD - your own "ruler" for success... or failure.

One MD is equal to three hits...

Some have 51 Heads and that's 0 MD as it didn't break the "barrier" of 53 hits.
Some have 54 Heads and that's +1 MD as it's more than 53 hits but not more than 56.
56 hits is the next level, the +2 MD barrier, so having 56 heads is still +1 MD while 57 is +2 MD.
And so on. And of course also the negative way for negative MD.

Now, that was "My Deviation"...

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



15. THE STANDARD DEVIATION - Part 1

What mathematicians have found and agreed upon, is a formula to calculate their "Standard Deviation" (SD for short).
And that wouldn't be worth a rat's a*s if it wasn't for the fact that their SD have some very interesting characteristics...

As I said; count-less (No! More!) of empirical studies have been done and they show this, and it can be replicated at any time by anyone (given there is a significant size of sample available) - and not just on roulette; anything measurable!

And with those characteristics as a basis... This is the consensus:

Breaking the 1 SD barrier is said to be equal to a 16% probability that the result is random
Breaking the 2 SD barrier is said to be equal to a 5% probability that the result is random
Breaking the 3 SD barrier is said to be equal to a 1% probability that the result is random
Breaking the 4 SD barrier and beyond is said to be a very small probability that the result is random

I bold "random" as that is what the SD is measuring: If the results are random (within normal fluctuation) or if they are "static" (have the ability to consistently stay positive or negative).

Now, here's where those characteristics I talked about come into play:
When an operation (a betting- or selection-method or any other thing that gives a measurable result on a random set of results) is at a positive SD and manages to STAY there, in many smaller samples, it may very well start to CLIMB towards +3 SD AND BEYOND given larger and larger samples.

For example:
You have a lot of 100-results samples for an "even" chance and you find yourself consistently being at 50 hits. Every 100-spins sample. If you check, you will find it is a positive SD of +0.27 in a 100-spins sample.
Now, if you take 10 such samples you get 500 hits in a 1000-results sample. That SD is at +0.85 - it is growing!
Ten 1000-spins samples having 500 hits each is 5,000 hits in 10,000 results. That is a nice +2.7 SD. Closing in at +3 SD...
And ten SUCH samples, each having 5,000 hits, is 50,000 hits in 100,000 results and THAT, my friend, is +8.55 SD! It grows a lot!

"Breaking the 4 SD barrier and beyond is said to be a very small probability that the result is random"
Think about that.

Now, to break the +3 SD barrier in no way means that your "operations" are MONETARY profitable... You saw it above as the "even" bet had a 0 profit in all samples but was at +8.55 SD.
(This is probability theory - not economics...)

The break-even, money-wise, for a single "even" bet at +3 SD goes at approximately 12,350 bets and 6,175 hits. (The "en prison" or "le Partage" rules are not considered)
For a single dozen or column bet, the figures are around 24,420 bets giving 8,140 hits.
A 6-number street bet breaks even at +3 SD just around 60,600 bets giving 10,100 hits.
Etc.
So just because you break the +3 SD barrier doesn't mean that your method is monetary a sound method. You have to break it quite quickly if you want to be profitable...

(So THAT is what we all are looking for: A method for roulette that consistently gives us so many hits that it quickly break the +3 SD barrier and goes beyond.)

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



16. THE STANDARD DEVIATION - Part 2

But that was money-talk; we're talking probability theory and they are very separate subjects...


Now, we were talking about the SPREAD of results, the deviation from the average.
A random deviation is agreed to never break the +-3 SD barrier and so the mathematical "prediction" for the results in a sample, is the expected mathematical average of the sample +-3 SD. Not an exact number any more, but a spread.

And here's how the SD is calculated:

SD = SQR(n * p * (1 - p))


Yeah, I know; it's a formula. But it's not really complicated - let me explain...

We have some letters there:
n = number of bets or predictions - we do NOT measure results for something not giving us results, like skipped spins.
p = the probability to hit - 18/37 or 1/37 or quite anything, really.
And then there is the "SQR", meaning the SQuare Root - check your calculator for the Square Root key - it's necessary if you want to do these calculations...

First look at the end: "(1 - p)". 1 minus the probability to hit. Do you remember? This is the way to calculate the probability for a miss.

In other words: the Standard Deviation is equal to "the Square Root of (number of spins times Probability to hit times Probability to miss)"

Supposing a Red bet for 1000 times, we solve the formula this way:
For Red to hit is p = 18/37 so the probability to miss is (1 - 18/37) = 19/37.
So now we can insert values for "n", "p" and "(1-p)"...

1000 * (18 / 37) * (19/37) = 249.82

And last you calculate the SQuareRoot of this 249.82 = 15.8

One SD = 15.8 hits.
The mathematical average is (18 / 37) * 1000 placed bets = 486.4 and so we add and subtract 15.8 to/from 486.4 to find the barriers:

+0 SD: 486.4 hits
+1 SD: 486.4 + 15.8 = 502.2 hits which means that if you have 503 hits you've broken the +1 SD barrier and has left the 0 SD level.
+2 SD: 502.2 + 15.8 = 518.0 hits which means that if you have 519 hits you've broken the +2 SD barrier and has left the +1 SD level.
+3 SD: 518.0 + 15.8 = 533.8 hits which means that if you have 534 hits you've broken the +3 SD barrier and has left the +2 SD level.
534 or more hits in a 1000-results sample... That's great.

The other way around for the negative SD:

-0 SD: 486.4 hits
-1 SD: 486.4 - 15.8 = 470.6 hits which means that if you have 470 hits you've broken the -1 SD barrier and has left the 0 SD level.
-2 SD: 470.6 - 15.8 = 454.8 hits which means that if you have 454 hits you've broken the -2 SD barrier and has left the -1 SD level.
-3 SD: 454.8 - 15.8 = 439.0 hits which means that if you have 439 hits you've broken the -3 SD barrier and has left the -2 SD level.
(Don't use that method...)

So for a 1000 results sample I (math) would estimate the number of hits being like 440 - 533, if the bet is Red or any other "even" bet.
And all of a sudden we have a practical way to measure results - not a theoretical fraction like 18/37 but an acceptable spread for the results.
Because if your results, using your betting-method or selection on one 1000 results sample, are within the boundaries of +-3 SD there is, really, no surprise. It is regarded random - could happen just anytime to anyone. But if it's consistently in the positive you should get more and larger samples - that's my recommendation.

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



17. RECORDED RESULTS

- OK OK OK! ENOUGH IS ENOUGH! You only talk math and probability and deviation and formulas and fractions that means - frankly - ABSOLUTELY NOTHING at the casino. The spins tell the truth!

Oooh... You want to do some REAL "reality checks" - EMPIRICAL STUDIES!
Glad you asked.

I have downloaded Spielbank Weisbaden results (table #3), April - Dec 2003, complete 2004, 2005, 2006 and 2007 plus Jan - July of 2008.
A total of 655,941 results over a period of 1,903 open days. [See the file-index in the Appendix]
(That was the most I could download from one table without trouble...)


- But no - they are past results, they are not valid! The only valid results are when you go to the casino and put money on the table!
- You mean that past spins cannot be used for empirical studies in this context?
- Yes! No! Old spins are old spins...
- So suppose I go to a casino, I bet and at the same time I note the results, counting Red hits. I find them to be 135 and that's a valid study in your opinion. But if I bring those results home and count the Red hits and find them to be 135 - then it's not valid any more??? Or do you mean that I will maybe find only 134?? Or 136???

I can see your point if I'm trying to develop a method to beat roulette. Then it would be all too easy to adopt that method to those results. That is called "backwards engineering" and is in reality a useless way to develop systems because the next sample of results may differ a lot from the first one.
But here I'm not backwards engineering anything - I simply count the occurrences of Red hits. Or whatever. They are the same if I'm recording at the casino or if I study the records at home, aren't they?


- But you don't know if there are errors! They may influence the end-result. You can only trust spins that you have recorded yourself.
- If there are errors, do you think they are very common? I don't - but of course it's impossible to know for us. We weren't there.

But! If they are few, they certainly "drown" in the 655,941 results sample and thus cannot influence the end result at all because what we look for occurs maybe thousands of times.
And should there be more than just a few you have to remember: Errors work both ways. Meaning that probably are not all errors noted as black numbers but as both red and black. They will probably even out at least to a degree and thus not influence the end result too much. Because what we look for occurs maybe thousands of times.

But you are correct: Spins that are verified are better. Can you get hold of a substantial amount of such spins; please let me know and I'll use them.

- "Substantial amount" - yeah... Why do you need millions and millions of spins. Not ONE living person will EVER make a gazillion bets in their whole life!
- You are correct there. Absolutely. But we're not interested in how many bets you will place in your life-time.

We are interested in FAIR studies.

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



18. FAIR EMPIRICAL STUDIES

Each and every possible combination shall have the possibility to be found in the sample.
That's only fair, isn't it?

And the more possibilities (more results) the more secure you can be that the result is not some fluke.
If what you count occurs only once in one 500 results sample - what does that tell you? That it is a 1/500 (0.2%) probability to hit always?
Maybe it was just a fluke and in the next 500 results it occurs ten times. Now it's suddenly a 1/50 (a whole 2%) probability... Or? How could you possibly tell?
Which sample contains the fluke? Maybe both. The figures are really too small to be sure.

Now suppose you check a 5,000,000 results sample and the same combination occurs 54,869 times, you have a much better figure to work with: 54869/5000000 (1.1% rounded).
Now, if something hits like 55,000 times in a sample and you have done nothing wrong when you count them, you can be rather sure that the result is representative for your combination.
You can have confidence in the results as you ran a FAIR study.

My PERSONAL opinion is that we would need absolutely NO LESS than (37 x 37 x 37) x (37 x 3) for a study of THREE-results, single-number bet, events. That's 5,622,483 events = 16,867,449 results!

Why? Because this amount gives every 3-spins event the possibility to occur 37 x 3 (111) times in average. That isn't much in terms of statistical security I admit that, but I wrote "no less than" and I mean it. 111 times in average is actually not a reliable amount - something like 11,111 possibilities would be a lot better.

This shows a problem when we want to empirically study something - who's got a results-collection of a large enough size?
My sample is, as I said, 655,941 results and gave 218,010 three-results events... Each LL combination has the possibility to occur 4.3 times... Let's hope it's enough as we check HL combinations.

The triple Zero (or any other three-numbers combination) should, mathematically, occur only 4.3 times in this size and kind of a sample - do you now realize how small it is?

Now you know why the larger sample is preferred before the smaller. And the larger the sample, the more realistic is the end result.

I mean; to empirically investigate the frequency of the combination "R-B-R" you wouldn't just use three spins, would you?
If they happen to be "B-R-B" your combination has a probability of 0 to hit at any time.
You obviously have to use a larger sample than that. Would you settle with any less than eight as there are eight possible combinations of R and B in three spins?

No, because if you randomly collect 8 three-results events, you can of course not be sure that there are all the eight different R/B combinations present - and that wouldn't be FAIR.
So you want a larger sample.
And so on. And so on...

And the sample should be random because we want a FAIR study, don't we? If so, the only good thing to do is to have as large a sample as possible. The bigger is ALWAYS the better.
(In this context...)


Whatever you think about Wiesbaden results: They give a rather significant sample size.
(And I have no other of this size - far from it)

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



19. MATH VS. REALITY

Sooo...

Do you remember the HL-table above, for three results?
We calculated the mathematical amount of LL in each HL, for example that the HL group "B-B-B" contained 5,832 LL combinations out of the 50,653 possible combinations.

In a perfect world, if we had 50,653 three-results events, there would be exactly 5,832 "B-B-B"s in that sample. But the world isn't perfect.
But how close to perfect is it?


In order to run the first "Math vs Reality" check I took the spins, starting April 1st 2003, of each day, starting at the first result and recorded them as "B" for Black, "R" for Red or "0" for Zero, in sequences of three.
If at the end of the day there were one or two spins left, they were discarded. The reason being that we don't know what happens while the casino is closed.

In the end I had 218,010 such 3-results events in the 1903 day-samples. [See the file-index in the Appendix]

As my combined (total) sample contains 218,010 three-results events each group would occur approximately 4.3 times their total of LL-combinations. Should. Mathematically. But do they?
I have checked.
(An empirical study!)

In the below table you can, for each group, see how many combinations they contain ("Combs"), the mathematical average number of occurrences there SHOULD be in the sample ("Math Ave") and the Standard Deviation ("StdDev").
You can also see the not-breaking -3 to +3 SD span, how many occurrences that was REALLY found in the sample ("Real") and the "broken" SD barrier ("SD") - if any.
Finally I show the difference between the Math average and the real number of occurrances, both in numbers ("Diff") and in percent ("Diff %"), compared to the Math average.

Group   Combs   Math Ave   StdDev   -3 SD   +3 SD     Real  SD      Diff   Diff %
---------------------------------------------------------------------------------
B-B-B =  5832   25100.86   149.03   24654 - 25547    25298  +1   +197.13    +0.78
B-B-R =  5832   25100.86   149.03   24654 - 25547    25116  +0    +15.13    +0.06
B-B-0 =   324    1394.49    37.22    1283 -  1506     1421  +0    +26.50    +1.90
B-R-B =  5832   25100.86   149.03   24654 - 25547    24921  -1   -179.86    -0.71
B-R-R =  5832   25100.86   149.03   24654 - 25547    25123  +0    +22.13    +0.08
B-R-0 =   324    1394.49    37.22    1283 -  1506     1407  +0    +12.50    +0.89
B-0-B =   324    1394.49    37.22    1283 -  1506     1389  -0     -5.49    -0.39
B-0-R =   324    1394.49    37.22    1283 -  1506     1467  +1    +72.50    +5.19
B-0-0 =    18      77.47     8.80      52 -   103       65  -1    -12.47   -16.09
R-B-B =  5832   25100.86   149.03   24654 - 25547    25159  +0    +58.13    +0.23
R-B-R =  5832   25100.86   149.03   24654 - 25547    24966  -0   -134.86    -0.53
R-B-0 =   324    1394.49    37.22    1283 -  1506     1387  -0     -7.49    -0.53
R-R-B =  5832   25100.86   149.03   24654 - 25547    25021  -0    -79.86    -0.31
R-R-R =  5832   25100.86   149.03   24654 - 25547    25041  -0    -59.86    -0.23
R-R-0 =   324    1394.49    37.22    1283 -  1506     1369  -0    -25.49    -1.82
R-0-B =   324    1394.49    37.22    1283 -  1506     1381  -0    -13.49    -0.96
R-0-R =   324    1394.49    37.22    1283 -  1506     1446  +1    +51.50    +3.69
R-0-0 =    18      77.47     8.80      52 -   103       72  -0     -5.47    -7.06
0-B-B =   324    1394.49    37.22    1283 -  1506     1419  +0    +24.50    +1.75
0-B-R =   324    1394.49    37.22    1283 -  1506     1367  -0    -27.49    -1.97
0-B-0 =    18      77.47     8.80      52 -   103       88  +1    +10.52   +13.58
0-R-B =   324    1394.49    37.22    1283 -  1506     1424  +0    +29.50    +2.11
0-R-R =   324    1394.49    37.22    1283 -  1506     1428  +0    +33.50    +2.40
0-R-0 =    18      77.47     8.80      52 -   103       71  -0     -6.47    -8.35
0-0-B =    18      77.47     8.80      52 -   103       84  +0     +6.52    +8.42
0-0-R =    18      77.47     8.80      52 -   103       77  -0     -0.47    -0.60
0-0-0 =     1       4.30     2.07       0 -    10        3  -0     -1.30   -30.29
---------------------------------------------------------------------------------
        50653  218010.00 (when all decimals are incl. Here: 218009.88)

I would say that the mathematical distribution is pretty close to the real. Wouldn't you agree?


I also gave examples of combinations that have the same probability as "0-0-0" and therefore should appear approximately the same number of times:

Group      Combs   Math Ave   StdDev   -3 SD   +3 SD     Real  SD      Diff   Diff %
------------------------------------------------------------------------------------
0- 0- 0 =     1       4.30     2.07       0 -    10        3  -0     -1.30   -30.29
1- 2- 3 =     1       4.30     2.07       0 -    10        9  +2     +4.70  +109.30
7-34-22 =     1       4.30     2.07       0 -    10        0  -2     -4.30  -100.00
25- 3-31 =     1       4.30     2.07       0 -    10        9  +2     +4.70  +109.30
36-36-36 =     1       4.30     2.07       0 -    10        5  +0     +0.70   +16.30

(Such small figures - "Real" - in only one collection are NOT to be taken too serious as they are not statistically sure, but they give an indication...)

That was how many times they appeared within the 3-results sample.
How many times did they appear if we used the results as continual sequences per day (break at the end of the day but we calculate the sample as 655,941 results):

Group      Combs   Math Ave   StdDev   -3 SD   +3 SD     Real  SD      Diff   Diff %
------------------------------------------------------------------------------------
0- 0- 0 =     1      12.95     3.60       3 -    23        9  -0     -3.95   -30.50
1- 2- 3 =     1      12.95     3.60       3 -    23       13  +0     +0.05    +0.39
7-34-22 =     1      12.95     3.60       3 -    23       14  +0     +1.05    +8.11
25- 3-31 =     1      12.95     3.60       3 -    23        8  -2     -4.95   -38.22
36-36-36 =     1      12.95     3.60       3 -    23       11  -0     -1.95   -15.06

(Such small figures - "Real" - in only one collection are NOT to be taken too serious as they are not statistically sure, but they give an indication...)


BTW, for the reader's knowledge: I was not personally the one who did the actual job making these tables - it was a computer-freak friend of mine who did.

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



20. CHECKING MY CLAIMS

For the next "Math vs Reality" check, let's consider what I claimed in the beginning:

If you make a 18/37 bet, you will have the probability to hit in 18/37 - no matter if you bet on the first, second or third trial.
You will always hit in 18/37 - as a mathematical average.


The math therefore also says that 18/37 three-results events in a sample will have a "R" in the first position, 18/37 will have a "R" at the second position and 18/37 will have it in the third.
As the sample-size (the three-results samples) is 218,010...

... the 18/37 Mathematical average = 106,058.92 (rounded) ...
... the SD = 233.37 and so ...
... the not-breaking -3 to +3 SD span is 105,359 - 106,759.


That's the math. What about reality?

Black in position 1: Found 106,207  +0 SD  +148.08 = +0.14%
                  2: Found 106,221  +0 SD  +162.08 = +0.15%
                  3: Found 106,096  +0 SD   +37.08 = +0.03%

Red in position 1: Found 105,842  -0 SD  -216.92 = -0.20%
                2: Found 105,805  -1 SD  -253.92 = -0.24%
                3: Found 106,031  -0 SD   -27,92 = -0.03%

Quite similar, I'd say... Not a quarter of one percent wrong either way...


More "Math vs Reality": What about only making a new bet (second or third) after a miss?

I claimed this to be true:

A: Making a first 18/37 bet of three, there is a 18/37 probability to hit at the first trial.
     So 18/37 of the 3-results events in the sample will do that. (As we actually just saw above)
     And 19/37 of the 3-results events in the sample will miss at the first trial.

B: Making a second 18/37 bet of three, there is a 18/37 probability to hit at the second trial, for the 19/37 that missed the first trial.
     So (18/37) x (19/37) of the 3-results events will do that.
     And (19/37) x (19/37) of the 3-results events will miss also at the second trial.

C: Making a third 18/37 bet of three, there is a 18/37 probability to hit at the third trial, for the (19/37) x (19/37) that missed the first AND the second trials.
     So (18/37) x (19/37) x (19/37) of the 3-results events will do that.
     And (19/37) x (19/37) x (19/37) of the 3-results events will miss also the third trial.

These are the Mathematical averages (in fractions). I will add and subtract 3 SD in order to make a mathematical "prediction" of the number of occurrences. And we will be able to see if math and probability differ very much from reality.
What do you think?


I used the following sample-sizes:

1: The first 100 three-results events of the file
2: The first 500
3: The first 1,000
4: The first 5,000
5: The first 10,000
6: The first 50,000
7: The first 100,000
8: All 218,010 three-results events of the file


The below table shows the results in the same format as above, for each trial (A - C) and the sample-sizes 1000, 10000 and all. And for both Black and Red...
[For a COMPLETE table incl all sample-sizes: See the Appendix - Table #1]


Bet   SampSize   Trial     Math Ave   StdDev    -3 SD    +3 SD     Real  SD      Diff   Diff %   Did NOT hit
------------------------------------------------------------------------------------------------------------
BLACK     1000       1       486.48    15.80      440 -    533      509  +1    +22.51    +4.62          491
           491       2       249.81    11.32      216 -    283      243  -0     -6.81    -2.72          248
           248       3       128.28     8.11      104 -    152      116  -1    -12.28    -9.57          132
               No hits       135.41     8.11      111 -    159      132  -0     -3.41    -2.51

BLACK    10000       1      4864.86    49.98     4715 -   5014     4871  +0     +6.13    +0.12         5129
          5129       2      2498.17    35.81     2391 -   2605     2542  +1    +43.82    +1.75         2587
          2587       3      1282.84    25.66     1206 -   1359     1264  -0    -18.84    -1.46         1323
               No hits      1354.11    25.66     1277 -   1431     1323  -0    -31.11    -2.29

BLACK   218010       1    106058.91   233.37   105359 - 106759   106207  +0   +148.08    +0.13       111803
        111803       2     54462.68   167.23    53961 -  54964    54386  -0    -76.68    -0.14        57417
         57417       3     27967.32   119.83    27608 -  28326    27910  -0    -57.32    -0.20        29507
               No hits     29521.06   119.83    29161 -  29880    29507  -0    -14.06    -0.04


Bet   SampSize   Trial     Math Ave   StdDev    -3 SD    +3 SD     Real  SD      Diff   Diff %   Did NOT hit
------------------------------------------------------------------------------------------------------------
RED       1000       1       486.48    15.80      440 -    533      461  -1    -25.48    -5.23          539
           539       2       249.81    11.32      216 -    283      270  +1    +20.18    +8.07          269
           269       3       128.28     8.11      104 -    152      138  +1     +9.71    +7.57          131
               No hits       135.41     8.11      111 -    159      131  -0     -4.41    -3.25

RED      10000       1      4864.86    49.98     4715 -   5014     4855  -0     -9.86    -0.20         5145
          5145       2      2498.17    35.81     2391 -   2605     2514  +0    +15.82    +0.63         2631
          2631       3      1282.84    25.66     1206 -   1359     1249  -1    -33.84    -2.63         1382
               No hits      1354.11    25.66     1277 -   1431     1382  +0    +27.88    +2.05

RED     218010       1    106058.91   233.37   105359 - 106759   105842  -0   -216.91    -0.20       112168
        112168       2     54462.68   167.23    53961 -  54964    54374  -0    -88.68    -0.16        57794
         57794       3     27967.32   119.83    27608 -  28326    28027  +0    +59.67    +0.21        29767
               No hits     29521.06   119.83    29161 -  29880    29767  +0   +245.93    +0.83

This was only ONE study performed on only ONE sample and other samples may give different results, but only within the boundaries of +-3 SD.
How I know? From personal experience (years...) plus results from all serious studies I have ever seen or read about. To date.

I ask:
* Do you think math is very different from reality?
* Do we really need to do such tiresome, time-consuming empirical studies or can we use a calculator?

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



21. FAVORABLE SITUATIONS - Part 1

- BUT NO! You can't just blindly look for Red - or whatever! In a casino you bet when the table is FAVORABLE to you.
- And when is that, then?

- Listen. I'll use your own math to show you a really GOOD method, based on a COMBINATION OF SEVERAL FAVORABLE situations: A method that will, in average -  yes, but you use averages too - bring you AT LEAST 98 units per 106 events of 7 trials each. (See; I can use your vocabulary)
- And how's that done?

- I'll use your OWN math: The probability for an "even" bet like Red to miss seven tries is calculated as:
(19/37) x (19/37) x (19/37) x (19/37) x (19/37) x (19/37) x (19/37) = well, something like 1/106.
So the probability to miss seven trials is one single event in every 106. In average.
Is this correct?

- Yes, it's absolutely correct. 100%...

- YES! I knew it! Now, here's my SPECIAL TWIST to find FAVORABLE SITUATIONS: I WAIT until I have SEEN FOUR NON-RED spins in a row and THEN I start betting Red. The first bet is 1 unit.
If that bet is lost because Red didn't hit I bet 2 units on Red. I have now bet a total of 3 units.
If that bet is also lost I make a third bet that is 4 units. On Red. I have now bet 7 units.

- So if all three bets are lost I have lost 7 units.
But this will happen ONLY ONCE in 106 - in average, that's your OWN math - and if any one of my three bets hits I have won 1 unit and that will happen in the other 105 cases.

So I win one unit 105 times and lose 7 units once = 98 units in profit for every 106 times I try it: Wait for four non-Reds and then bet Red for up to three times.

Plus and Minus that "3 SD" you mathboyzzz like to use as a safety-net. Now I'll do that too. Hah! And so I have calculated the Standard Deviation like:

3 SD = 3 x SQR(trials x (1/106) x (105/106))

...because the chance to HIT a seven-spins MISS = 1/106... Got that?
(Y'see - I learn!)
SO! YOUR OWN math shows that I will win. And win A LOT!

I have ANOTHER thing working for me here as well: When Red hasn't shown for four sprins, it GENERALLY comes within three more.
I have seen this in the casino sooo many times it must be considered a truth.
HAH!

And a last thing: Empirical studies! They show that events even out over time and therefore Red SHOULD hit more than average after not been seen for a while. As you have collected sequences that have no Reds AT LEAST in the first four results, there is a BIG difference between Red and Black so it HAS to even out in the last three results.

There you are!
What do you say? Do you DARE check it? I've got YOUR math on MY side now!


- OK... So you want me to collect 7-spins sequences where there is no Red within the first four.Then check the next three for Red.
I will collect them in the same manner as the 3-results sequences: I'll start at the first result each day and if there are any left-overs so I cannot collect a complete 7-results sequence at the end of the day I will discard the last spins. Each and every day.

- Exactly! And do it for Black as well!

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



22. FAVORABLE SITUATIONS - Part 2

I looked into the file and...
...for the four non-Reds, I found a total of 21,355 events in the file.
...for the four non-Blacks, I found a total of 21,157 events in the file.

This is due to how I collected them: I looked for the four non-Red, recorded them and the next three results. Then I started at the NEXT result, looking for another sequence of four non-Reds.
It is possible to find more events if I, after recording one event, went BACK to the result IMMEDIATELY AFTER the first one of the last recorded event.

That way gives us a considerably larger sample-size and that would be an advantage but has the disadvantage that many of the seven-spins events are part of each-other and thus may influence the end-result in a non-preferred way.
We have to settle with the "discrete" events.


- You know; I'll make my own prediction for this study... Actually, I will predict that the results from this study will be very similar to the THREE-results study above... Remember that one? That's my "prediction" for this study... Exactly the same as above...


SampSize         Math Ave  StdDev   -3SD   +3SD
-----------------------------------------------
  100   No hits     13.54    2.56      5 -   21 ... You say:   0 -   3
  500   No hits     67.70    5.73     50 -   84 ... You say:   0 -  11
1000   No hits    135.41    8.11    111 -  159 ... You say:   0 -  18
5000   No hits    677.05   18.14    622 -  731 ... You say:  27 -  67
10000   No hits   1354.11   25.66   1277 - 1431 ... You say:  66 - 123
21157   No hits   2864.90   37.33   2752 - 2976 ... You say: 158 - 241
21355   No hits   2891.71   37.50   2779 - 3004 ... You say: 160 - 243

Who do you think is correct - our figures differ A LOT...?

.
.
.

And NOW <drum-roll here> the REEESULTS:

[For COMPLETE tables incl all three sample-sizes: See the Appendix - Table #2]

No RED in the first four:
Bet   SampSize          Math Ave   StdDev    -3 SD    +3 SD     Real  SD      Diff   Diff %
-------------------------------------------------------------------------------------------
RED        100 No hits     13.54     2.56        5 -     21       15  +0     +1.45   +10.77
RED        500 No hits     67.70     5.73       50 -     84       64  -0     -3.70    -5.47
RED       1000 No hits    135.41     8.11      111 -    159      131  -0     -4.41    -3.25
RED       5000 No hits    677.05    18.14      622 -    731      649  -0    -28.05    -4.14
RED      10000 No hits   1354.11    25.66     1277 -   1431     1323  -0    -31.11    -2.29
RED      21355 No hits   2891.71    37.50     2779 -   3004     2882  -0     -9.71    -0.33

Bet   SampSize          Math Ave   StdDev    -3 SD    +3 SD     Real  SD      Diff   Diff %
-------------------------------------------------------------------------------------------
BLACK      100 No hits     13.54     2.56        5 -     21       10  -0     -3.54   -26.15
BLACK      500 No hits     67.70     5.73       50 -     84       66  -0     -1.70    -2.51
BLACK     1000 No hits    135.41     8.11      111 -    159      128  -0     -7.41    -5.47
BLACK     5000 No hits    677.05    18.14      622 -    731      639  -0    -38.05    -5.62
BLACK    10000 No hits   1354.11    25.66     1277 -   1431     1330  -0    -24.11    -1.78
BLACK    21355 No hits   2891.71    37.50     2779 -   3004     2849  -0    -42.71    -1.47

No BLACK in the first four:
Bet   SampSize          Math Ave   StdDev    -3 SD    +3 SD     Real  SD      Diff   Diff %
-------------------------------------------------------------------------------------------
BLACK      100 No hits     13.54     2.56        5 -     21       15  +0     +1.45   +10.77
BLACK      500 No hits     67.70     5.73       50 -     84       73  +0     +5.29    +7.81
BLACK     1000 No hits    135.41     8.11      111 -    159      132  -0     -3.41    -2.51
BLACK     5000 No hits    677.05    18.14      622 -    731      676  -0     -1.05    -0.15
BLACK    10000 No hits   1354.11    25.66     1277 -   1431     1331  -0    -23.11    -1.70
BLACK    21157 No hits   2864.90    37.33     2752 -   2976     2840  -0    -24.90    -0.86

Bet   SampSize          Math Ave   StdDev    -3 SD    +3 SD     Real  SD      Diff   Diff %
-------------------------------------------------------------------------------------------
RED        100 No hits     13.54     2.56        5 -     21       10  -0     -3.54   -26.15
RED        500 No hits     67.70     5.73       50 -     84       60  -0     -7.70   -11.38
RED       1000 No hits    135.41     8.11      111 -    159      118  -0    -17.41   -12.85
RED       5000 No hits    677.05    18.14      622 -    731      679  +0     +1.94    +0.28
RED      10000 No hits   1354.11    25.66     1277 -   1431     1365  +0    +10.88    +0.80
RED      21157 No hits   2864.90    37.33     2752 -   2976     2913  +0    +48.09    +1.67


Again, I ask:
* Do you think math is very different from reality?
* Do we really need to do such tiresome, time-consuming empirical studies or can we use a calculator?

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



23. ...WHERE ARE THEY?

- But then your math DOESN'T WORK!!! Why did I miss so many? You said that my calculations were correct!
- No, I said that your calculation that "Red wouldn't hit for seven spins in 1/106" (approximately) was correct. And I say again that it is.
BUT!
Then, after that, you said that you were going to WAIT for four spins without a Red... You didn't ask me about that.


What you didn't realize was that you all of a sudden had four KNOWN results. Do you remember what I said about known results, in the beginning?
A known result is a certainty and as such we always calculate it as 1/1.

Look here: ALL the sequences that hadn't got a Red in the first four trials, could be said to look like this if we put all of them in one big HL (High-Level - remember?) combination:

Result 1: B0 <--- Black or Zero hit here
Result 2: B0 <--- The same
Result 3: B0
Result 4: B0
Result 5: ? <--- Result not known yet
Result 6: ?
Result 7: ?

Now this HL group consists of a lot of LL 4-number results, for example "17-24-0-8" or "33-11-2-29"... And this is where you are when you start betting.
Now: By which three-result combinations can that four-spins, non-Red, sequence you have just seen, end to make it a complete seven-spins sequence?
What are the possible results AFTER "17-24-0-8" or "33-11-2-29"?

- Well, "B-B-B", "B-B-R", "B-B-0"... Wait a minute! I remember this...?
- Yes, we've seen this before: All of a sudden we're back at this table:

B-B-B  -  5,832 p = 5832/50653 = .115136 (11.5%)
B-B-R  -  5,832
B-B-0  -    324 p = 324/50653 = .006396 (0.64%)
B-R-B  -  5,832
B-R-R  -  5,832
B-R-0  -    324
B-0-B  -    324
B-0-R  -    324
B-0-0  -     18 p = 18/50653 = .000355 (0.036%)
R-B-B  -  5,832
R-B-R  -  5,832
R-B-0  -    324
R-R-B  -  5,832
R-R-R  -  5,832
R-R-0  -    324
R-0-B  -    324
R-0-R  -    324
R-0-0  -     18
0-B-B  -    324
0-B-R  -    324
0-B-0  -     18
0-R-B  -    324
0-R-R  -    324
0-R-0  -     18
0-0-B  -     18
0-0-R  -     18
0-0-0  -      1 p = 1/50653 = .00002 (0.002%)
---------------
     RC: 50,653 = (37 x 37 x 37) = Correct

Are OTHER combinations or other numbers of LL in this HL possible, to end our seven-spins sequence after the first four results are known...?
No, of course not - there are no other or no less - and that's why I could simply use the same figures I used to "predict" the number of lost 3-trials events. Because there were only three trials left AFTER you had seen the first four.

None of these combinations (not HL nor LL) can be excluded or changed in any way because you have happened to see a four non-Red or non-Black sequence, right?
And if none of them can be excluded or changed, no other combination can have a higher probability than usual to hit, can it? Will the sum still be 100% if that is the case?

Or the four spins you have just seen; can they in some way influence the results of the coming three?
("Hey Ball" says the wheel, "Red didn't hit for four spins, now jump to a red number - it is due, you know")
No, of course not.

The sad truth is: When you HAVE seen the first four results of seven, only three results are FUTURE and so the seven results can only end in (37x37x37) ways.

Please study this empirically on a sufficient number of your own results (remember what I said about a fair study?) if you don't believe me...

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



24. IT WILL EVEN OUT IN THE LONG RUN

- But it happens so often in the casino. I have seen it a gazillion times! We ALL have.
- No, in reality not. You're a victim of something called "selective memory" - you notice things that you are looking for or that is special to you but you DON'T remember all the gray dull stuff that happens all the other time.
Do this: Bring pen and paper to the casino and record every time the Red comes within three spins and every time it doesn't, after not been seen for four spins. It will not take long before you realize things: When you record, the phenomenon doesn't occur that often at all.

Do you think the results are influenced by the fact that you or someone else are recording or do you think the results were, in fact, the same all the time?


- But it should even out! At least a little and that SHOULD have been noticeable in the study. The Blacks are so many more in the first four...
- Well, actually probability theory doesn't say that anything WILL even out. It says that you can calculate a PROBABILITY for it. A high probability? Let's use an example for this:

Suppose that you, after seeing 10 spins have counted 6 Reds, 3 Blacks and 1 Zero. Now you have a 3-hits difference between Red and Black. For this to even out you will need 3 more Blacks than Reds. So to even out you will need AT LEAST 3 spins - more if they are not all Blacks. Now, do you know the probability to have MORE Black hits than Red, in three spins? (As that's when you will at least start to even out - and at least by one hit)

Yes you do! You can see that in the three-trials table above. Look for all combinations that have more "B"s than "R"s.

B-B-B  -  5,832
B-B-R  -  5,832
B-B-0  -    324
B-R-B  -  5,832
B-0-B  -    324
B-0-0  -     18
R-B-B  -  5,832
0-B-B  -    324
0-B-0  -     18
0-0-B  -     18
---------------
         24,354 / 50,653 - less than 50%...

Because the probability to hit is only 18/37 - not 50% - there is a greater chance that you will STAY or even be MORE BEHIND, than that you will at least START to even out...
But if you look at it in PER CENT it will probably be correct: A difference of 10 in 200 is 5% but a difference of 50 in 2000 spins is half; only 2.5%. In this case you have to ask yourself: Do I hit in per cent or do I hit in numbers? Is the per cent DEcreasing? Is the number of hits really INcreasing?

Which question is more interesting to you???

I used this example as we already had done all the maths. It is, however, possible to extend it to any bet and any difference and the results will always be the same:
If the probability to hit is LESS than 50%, the chance to even out IN NUMBERS is also less than 50%...

The opposite is of course also true:
If the probability to hit is HIGHER than 50%, the probability to even out IN NUMBERS is also above 50%.

Ask yourself: Can I have a higher probability to hit, just because I try to even out?

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



25. THE WAKE-UP

I did a special study to show that the "even-out" theory is, in fact, a myth if you have less than 50% probability to hit:

On a day-basis^* I checked numbers that hadn't hit for at least 74 spins. When they hit for the first time after that (the "wake-up hit") I counted how many times and when it hit again, within the next 37 spins.
The theory being that a number that hasn't hit for a long time should even out.

It is also to show that saying things like:
"We have all seen sleepers hit like crazy after waking up, haven't we? It happens all the time"...
...in reality is the result of a selective memory.

There were a total of 52,408 "wake-ups" in the file, of which 33,401 had at least one hit within the next 37 spins.

An excerpt of the results:
[For a COMPLETE table incl all spins: See the Appendix - Table #3 (Also shows distribution of the first and all hits)]

How long before the FIRST hit comes AFTER the wake-up hit? (37 spins max wait)

Spin   Math ave   StdDev    -3SD to +3SD     Real  SD      Diff  Diff %
------------------------------------------------------------------------
   1    1416.43    37.12    1306 -  1527     1443  +0    +26.56   +1.87
   2    1378.15    36.61    1269 -  1488     1394  +0    +15.84   +1.15
   3    1340.90    36.12    1233 -  1449     1343  +0     +2.09   +0.15
.
.
.
  35     557.98    23.30     489 -   627      543  -0    -14.98   -2.68
  36     542.90    22.98     474 -   611      524  -0    -18.90   -3.48
  37     528.23    22.67     461 -   596      548  +0    +19.76   +3.74
------------------------------------------------------------------------
                                      Sum:  33401
0 hits 19016.31    22.67   18948 - 19084    19007  -0     -9.31    -0.04
------------------------------------------------------------------------
                                      Sum:  52408

Frankly: Nothing hits like crazy here. Math average estimated 9.31 losses too little - estimating in the 19,000 misses range!
Four hundredths of one percent wrong.

(To really see that nothing out of the ordinary happens, you should study the complete table in the Appendix)


So (for the last time) I ask you:
* Do you think math is very different from reality?
* Do we really need to do such tiresome, time-consuming empirical studies or can we use a calculator?

(Well... that second question is really asked by my friend who is making these tables...)


^*) What I mean by "day-basis" is that I ended everything at the end of the day and discarded everything that was not complete. The reason to discard was that I didn't want "broken" 37-spins results. A number that hits for the first time after 180 spins and gets only 20 possibilities to occur because the day ends - that isn't fair.
And I want to do this in a fair way.

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



26. MISDIRECTED INTUITION

To sum it all up:
You did one of the most common mistakes in the business... You mixed STATISTICS and PROBABILITY - you mixed certainty and UNcertainty...
And you simply cannot handle those two the same way, like you did.

The method to wait some spins in order to detect something (like 4 non-Red spins, a "wake-up hit" or actually whatever) in order for something else or the same to happen because it is "due to happen", is generally called "Gambler's fallacy", partly because that's what it is - a true fallacy, as you could see for yourself - and partly because mostly (ignorant and/or greedy) gamblers fall for it.

It is often seen in gambling forums (I heard it's called "Forum mathematics" by some...) posted by members who don't know how the logics, math and reality work and so they do it out of ignorance.
Have mercy on them...

The figures you get, calculating like you did, are very enticing and the math looks really sound, I admit that.
But nevertheless it has nothing in common with reality.

This kind of enticing logics and math has even got an official name ("Gambler's fallacy" aside) and that is "Misdirected intuition", named by C G Hempel (1905 - 1997).
(A translation from my language - maybe not the exact English name. Please enlighten me...)


Misdirected intuition...
Says it all.


And here's a friendly warning:
There is one group of people who FREQUENTLY use and defend "Misdirected intuition / Gambler's fallacy" arguments and the adherent skewed logics and math: Roulette Systems Peddlers!
As I said; the "probabilities" are enticing and the logic and math looks sound so of course they use it! But do you think that the peddlers don't know it's a fallacy?
Not in a long shot. They know.

Because they HAVE tested their systems/methods in a FAIR way, haven't they?
Using a sample of a size that makes it fair? Sure... (Ask them how big the sample was...)

Either they have, and in that case they KNOW they are LYING.
OR they sell a system/method they haven't studied properly. And how great is that?
Have mercy on their customers...


Misdirected intuition...
Something is due to happen. Says who?

Logics? No.
Logics says "There are 37 numbers each spin with equal chances to hit."

Math? No.
Math says "p = covered bets / 37"

Fair empirical studies? No.
Fair empirical studies say: "We agree with Logics and Math... +-3 SD, that is"

Roulette system peddlers? Yes.
I wonder why...

[Kon-Fu-Sed]

Roulette Probability Made Easier
By Kon-Fu-Sed, 2008, for the VLS forum members



27. THE END

Now, my friend, we are at the end of this... We've returned to our 3-results table and it means that that's all - from now on it's only variations of the theme.
You can use the same logics and math on any kind of bet and any sample-size of significance - they are the same in all situations.


I really hope I have been able to enlighten you a little and shown that logics, math and reality in fact are close to the same. (Well, plus/minus 3 SD...)
And I hope you've learn how you can use logics and math to calculate the probabilities of different events and be comfortable with the results you get - whatever they are. And that you DO it, of course.
Also; I hope that you know how to interpret the results you get correctly.

And thus it's also possible for you to, in a very simple way, decide if a system/method is at least worth a study.
And you can do FAIR empirical studies and know how to interpret the results in a correct way, because you understand the value of a fair study that gives fair results. I hope.

And last, but not least, I hope I have given you an arsenal of weapons against those systems peddlers who's income from "roulette" goes via your wallet.
At least you can see through their "99.9% winning rate" promises in no-time.
(You can do even better: Simply betting on the 1st dozen and High for six times gives you a 99.995% chance to hit!
Sell it to them!)


As a final hint for you, that will help you A LOT through the every-day basic calculations that we've done above:
Use Grabb's tools! You find them here:
nolinks://vlsroulette.com/grabb/

The "Hit or Sleep" and the "Standard Deviation" tools are super for those simpler calculations you do every day.

For the more complicated, though, you'll still need your calculator.


- But... but... WAIT! You can't stop now, because now I've done all sorts of calculations on all sorts of bets and I have studied recorded spins empirically and I simply CANNOT find anything that is winning... That's no fun. Do I have to give up roulette???

- No, of course not. If you like to play, why not play? The difference from before is that you now know that it's a LEISURE-game. It's a MATH GAME with the odds in favor of the casino, and I told you in the beginning that the math works - and will work - "as long as the wheel and ball are fair and the dealer doesn't aim for certain parts of the wheel (with more success than random)...".
That may be something to remember.

Maybe you should, while you are leisure-playing, study the wheel, ball and dealer in close detail to see if maybe, just maybe, there is something making the game not-so random. Is the dealer shooting the ball in a consistent way? Is it predictable? Does the ball hit only a few deflectors? Is the wheel level? Is the wheel and ball in perfect condition? Is that spot grease?

Ask yourself these and more questions - be curious. And why not? You are just leisure-playing anyway, so you can think more of the future games than on the present - and maybe you'll go from playing a math-based game to a physics-based game.

Methods based on logics and math cannot - WITHOUT LUCK - give you a real advantage as REALITY shows.
Maybe methods based on physics can?

But that's a completely different story.


Good Luck, my friend, and I hope YOU will find that method that for ever breaks the +3 SD barrier.

See You On-Board!
Kon-Fu-Sed

VLS forum member


If s**t can happen, s**t will happen.
- But when it hits the fan, probability theory is like having an umbrella.

[Kon-Fu-Sed]

-